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3 November, 07:58

The sum of an infinite geometric series is 450, while the common ratio of the series is 4 / 5. What is the first term of the series? A) 22 1 2 B) 45 C) 90 D) 180

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  1. 3 November, 09:00
    0
    C) 90

    Step-by-step explanation:

    The sum of an infinite geometric series is:

    S = a₁ / (1 - r)

    where a₁ is the first term and r is the common ratio.

    450 = a₁ / (1 - 4/5)

    450 = a₁ / (1/5)

    450 = 5a₁

    a₁ = 90
  2. 3 November, 09:29
    0
    answer is 90 for first term

    Step-by-step explanation:

    Let the terms be

    First term x

    We will use the formula s∞=x/1-r to find the sum of an infinite geometric series, where - 1
    We know the sum and the common ratio, so we'll be solving for x where r = 4/5

    s∞=x/1-r

    450=x/1-4/5

    450=x/1/5

    450=5x

    x=90

    this is the first term x1 = 90

    we know that common ratio is 4/5, so multiplying the first term by factor 4/5 to get the second term

    90 x 4/5 = 72 second term
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